Heron's Formula

We have a school project on The Applications Of Heron's FormulaIt has to contain a minimum of 5 pages apart from the introductionI replace 1 of them with the proof.Please show me how can I prove it And in the other 4 pages we have to show various Applications of the FormulaCould you suggest some of them

P.S.: Please give a proof without any Trigonometry and pls don't recommend that which is given in Wikipedia because I didn't understand it

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.''God exists because Mathematics is consistent, and the devil exists because we cannot prove it''You have made another human being happy. There is no greater accomplishment.' -bobbym

Re: Heron's Formula

Hi Agnishom

You could put an example on one page. An application on a quadrilateral on another.

Oh, and, I recommend reading the Wikipeadia article on it.

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: Heron's Formula

So I can fill 2 of the 4 pages: 1 with a simple example & the other with an example on QuadrilateralPlease give two other applications( May be two interesting problems)

Please explain the proofI don't understand what's written on Wikpedia

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.''God exists because Mathematics is consistent, and the devil exists because we cannot prove it''You have made another human being happy. There is no greater accomplishment.' -bobbym

Re: Heron's Formula

I have to say that don't remember. I will read the Wikipedia article and then try to explain it to you.

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: Heron's Formula

It's kinda interesting that the formula lets you know whether or not you have a legitimate triangle.If it gives zero then it indicates that you have a "pretty doggone flat triangle." Eg. 4,5,9.It gives a negative number under the radical when it can't be a triangle. Eg. 4,5,10.

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

Re: Heron's Formula

Hi Agnishom

Which of this don't you understand:

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: Heron's Formula

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.''God exists because Mathematics is consistent, and the devil exists because we cannot prove it''You have made another human being happy. There is no greater accomplishment.' -bobbym

Re: Heron's Formula

No I can understand it the way it is proved using Pythagoras

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.''God exists because Mathematics is consistent, and the devil exists because we cannot prove it''You have made another human being happy. There is no greater accomplishment.' -bobbym